Compact, energy efficient Mach-Zehnder interferometers and optical attenuators

ABSTRACT

Mach-Zehnder interferometers comprise heater elements configured to have projections in the plane of optical waveguides positioned such that two adjacent sections of one optical waveguide arms are heated by a common heater element. The heater and at least a substantial section of the heated waveguide segments can be curved. Configurations of an optical waveguide arm can comprise an outer curved heated section, an inner curved heated section, and a loopback waveguide section connecting the outer curved heated section and the inner curved heated section, with average radius of curvature selected to form an open accessible space. Appropriate configurations of the two optical waveguide arms provide for nested configurations of the arms that provide for a compact structure for the interferometer.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. provisional patent application62/437,110 filed Dec. 21, 2016 to McGreer et al., entitled “CompactPhase Shifters and Corresponding Mach-Zehnder Interferometers,”incorporated herein by reference.

FIELD OF THE INVENTION

The invention relates to Mach-Zehnder Interferometers with thermo-opticphase shifters in a planar lightwave circuit which can find applicationin optical telecommunication systems. The invention further relates toplanar lightwave circuits providing variable optical attenuation withefficient power use.

BACKGROUND OF THE INVENTION

Optical components providing a given function for fiber opticalcommunications are progressing towards smaller size with less electricalpower consumption. Integrated optical technology such as planarlightwave circuits is a key enabler of this progress. The planarlightwave circuit (PLC) generally is formed on a flat substrate.Materials can be patterned to form optical waveguides that willconstrain light of an appropriate wavelength range so that the light maybe guided along optical pathways defined by a core material of thewaveguide. Types of optical waveguides include, but are not limited to,ridge waveguides, rib waveguides, and channel waveguides. As oneexample, a channel waveguide with a rectangular cross section maycomprise a silica core region surrounded by a silica cladding regionwherein the index of refraction of the core region is higher in valuethan that of the silica cladding region. In such an example, thepercentage difference between to two values of index of refraction maybe referred to as the index contrast. This particular example may beused to exemplify particular design considerations which may be modifiedto suit a particular situation by one practiced in the art. However, asknown in the art, many other waveguide variations are possible and manyother materials suitable for forming optical waveguides (includingsilicon, InP, various polymers, and various other glass materials) arepossible.

Many useful functions within a PLC are provided by static devices;conversely, some functions require dynamic control from circuitryexternal to the PLC. A thermo-optic phase shifter is a common devicethat enables dynamic control of various optical functions. Typically, athermo-optic phase shifter is formed by depositing a thin film of metalonto the top cladding above the optical waveguide. The metal film orsemiconductor film can be patterned to define the boundaries of theheater, and herein is referred to as the “heater.” Desirable metalmaterials for heaters resist corrosion and are generally durable, suchas tungsten, nickel-chromium alloys (nichrome), and other metals, suchas those known in the art. Methods for forming heaters for PLCs includedeposition by sputtering, other physical vapor deposition, or othersuitably process followed by patterning.

One of the commercially significant devices integrated onto a PLC is aMach-Zehnder interferometer (MZI). Providing an MZI with an opticalphase shifter on one or both of the arms of an MZI can provide dynamiccontrol over some aspects of the MZI function. A number of optical phaseshifters are known in the art, including, but not limited to,thermo-optic phase shifters, carrier injection phase shifters, andcarrier depletion phase shifters. The transfer function of the MZI isdependent upon the phase shift of the first arm relative to the phaseshift of the second arm. In particular, the transfer function of the MZIdepends on the differential phase shift and is substantially independenton the amount of phase shift that is common to both arms. When the MZIis configured with at least one thermo-optic phase shifter, the functionof the phase shifter is to introduce a temperature difference betweenthe first arm and the second arm and thereby determine the MZI transferfunction. An MZI with a phase shifter on one or both arms may be used asan optical switch or, alternatively, as a variable optical attenuator(VOA).

SUMMARY OF THE INVENTION

In a first aspect, the invention relates to a planar lightwave circuitcomprising a Mach-Zehnder interferometer along a plane of the circuit,the Mach-Zehnder interferometer comprising an input optical coupler, anoutput optical coupler, a first optical waveguide arm opticallyconnecting between the input optical coupler and the output opticalcoupler, a first heater configured to heat both the outer curved heatedsection and the inner curved heated section of the first opticalwaveguide arm, and a second optical waveguide arm not heatedsignificantly by the first heater and optically connected between theinput optical coupler and the output optical coupler. In someembodiments, the first optical waveguide arm comprises an outer curvedheated section, an inner curved heated section, and a loopback waveguidesection connecting the outer curved heated section and the inner curvedheated section. The outer curved heated section and inner curved heatedsection can be adjacent each other with the inner curved heated sectionhaving a smaller average radius of curvature than the outer curvedheated section and a larger average radius of curvature than theloopback waveguide section such that an open accessible space enclosedin part by the arc of the inner curved heated section. In someembodiments, the second optical waveguide arm comprises an outer curvedsection, an inner curved section adjacent the outer curved section and aloopback waveguide section, at least a portion of the loopback waveguideof the second optical waveguide arm being located in the open accessiblespace of the first optical waveguide arm.

In a further aspect, the invention pertains to a planar lightwavecircuit comprising a Mach-Zehnder interferometer along a plane of theplanar lightwave circuit the Mach-Zehnder interferometer comprising aninput optical coupler, an output optical coupler, a first opticalwaveguide arm optically connecting between the input optical coupler andthe output optical coupler, a first heater associated with the firstwaveguide arm, and a second optical waveguide arm optically connectingbetween the input optical coupler and the output optical coupler, inwhich the second optical waveguide is not significantly heated by theheater. The first optical waveguide arm can comprise an outer curvedheated section, an inner curved heated section adjacent the outer curvedheated section, and a loopback section connecting the outer curvedheated section and the inner curved heated section. The first heater canbe positioned to significantly heat both the outer curved heated sectionand the inner curved heated section of the first waveguide arm, in whicha projection of the heater in a plane of the waveguides is curved.

In another aspect, the invention pertains to a planar lightwave circuitcomprising a Mach-Zehnder interferometer along a plane of the circuit,the Mach-Zehnder interferometer comprising an input optical coupler, anoutput optical coupler, a first optical waveguide arm opticallyconnecting between the input optical coupler and the output opticalcoupler, a first heater, and a second optical waveguide arm opticallyconnecting between the optical splitter and the optical coupler. Thefirst heater generally is on cladding over the waveguide core that isassociated with the first waveguide arm. A projection of the firstheater into the plane of the first waveguide arm can be positioned inthe plane between two adjacent sections of the first waveguide arm, therelative positions of the adjacent sections specifying inner edges ofthe adjacent waveguide sections closest to the adjacent waveguidesection and outer edges furthest from the adjacent waveguide sectionperpendicular to the light path, and with an extent of the heater in theplane no further than the outer edges of the adjacent sections of thefirst waveguide arm. Generally, the second optical waveguide is notsignificantly heated by the first heater.

The improved designs described herein rely on innovative waveguidelayouts that provide for efficient packing of the devices on the planerstructure, while maintaining functional isolation between the respectiveelements to result in improved energy efficiency.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a functional schematic top view of an embodiment of aMach-Zehnder interferometer (MZI) comprising thermo-optic phase shifterson each MZI arm with a schematic indication of waveguide sections thatcan be configured adjacent to each other for an energy conservingcompact structure.

FIG. 2 is a layout schematic top view of an embodiment of an MZIcomprising two thermo-optic phase shifters in which two segments of eachMZI arm are positioned close to each other for heating with a commonheater and in which a loopback waveguide section joins the adjacentcommonly heated section.

FIG. 3 is a schematic top view of an energy efficient thermo-optic phaseshifter of FIG. 2 separated from the MZI structure with two curvedheated sections that are positioned adjacent to a common heater.

FIG. 4 is a schematic cross sectional view of the thermo-optic phaseshifter in FIG. 3 taken along line A-A with a first embodiment of aheater that extends in the plane over and past the heated waveguidesections.

FIG. 5 is a schematic cross sectional view of the thermo-optic phaseshifter of FIG. 3 taken along line A-A with an alternative embodiment ofa heater, in which the heater is over both a first waveguide and asecond waveguide with aligned outer edges.

FIG. 6 is a schematic cross sectional view of the thermo-optic phaseshifter of FIG. 3 taken along line A-A with a further alternativeembodiment of a heater, in which the heater partially extends over botha first heated waveguide and a second heated waveguide.

FIG. 7 is a schematic cross sectional view of the thermo-optic phaseshifter of FIG. 3 taken along line A-A with another alternativeembodiment of a heater, in which the heater along the plane of thedevice is between a first heated waveguide and a second heatedwaveguide.

FIG. 8 is a schematic cross sectional view of the thermo-optic phaseshifter of FIG. 3 taken along line A-A with a heater having two heatingelements separated by a gap that is between the first heater waveguidesection and the second heated waveguide section, in which each heaterpartially covers a portion of a respective heated waveguide sectionalong the plane of the device.

FIG. 9 is a schematic top view of the thermo-optic phase shifter of FIG.3 depicting a first configuration of electrical interconnects to powerthe heater.

FIG. 10 is a schematic top view of the thermo-optic phase shifter ofFIG. 3 with a heater having two heating elements divided along the arcof the curved heated waveguide sections depicting a configuration ofelectrical interconnects to power the two heating elements.

FIG. 11 is a schematic top view of the thermo-optic phase shifter ofFIG. 3 with a heater having two heating elements divided along the widthof the waveguide path of the curved heated waveguide sections, such asshown in FIG. 8, depicting a configuration of electrical interconnectsto power the two heating elements.

FIG. 12 is a top view of a prior art MZI in which each MZI arm has athermo-optic phase shifter in which three adjacent sections of waveguideare simultaneously heated with a single heater.

FIG. 13 is a schematic top view of an MZI in which the energy efficientphase shifters of FIG. 2 are reconfigured to provide an open accessiblespace that provides for intertwining of the MZI arms through the use ofthe open accessible space.

FIG. 14 is a schematic top view of an MZI with phase shifters onrespective arms of the MZI in which the phase shifters are rolledtogether in a compact format without significant optical or thermalinterference between the respective arms with illustrated portionsincluding the input coupler, the two MZI arms, and the output coupler.

FIG. 15 is a schematic top view of the MZI of FIG. 14 with the paths ofthe waveguide of each MZI arm parameterized to provide for a convenientdescription of features of the waveguides.

FIG. 16 is a schematic top view of the MZI of FIG. 14 in which one MZIarm is removed to provide a clearer view of geometrical parameters toenable a compact footprint.

FIG. 17 is a schematic top view of the MZI of FIG. 16 with the depictedarm rotated 180 degrees to form the MZI of FIG. 14 emphasizing theability of the second arm to nest within accessible open space of thefirst arm.

FIG. 18 is a schematic top view of the phase shifters of the MZI of FIG.14 emphasizing the Yin Yang characteristic of the configuration.

FIG. 19 is a schematic top view of the MZI of FIG. 14 illustrating thecompact footprint that is possible with this configuration.

FIG. 20 is a schematic cross section view of a thermo-optic phaseshifter as described herein further comprising trenches to provideadditional thermal isolation of the heated section.

FIG. 21 is a schematic view of an input coupler comprising a Y-branch.

FIG. 22 is a schematic view of an input coupler comprising a directionalcoupler.

FIG. 23 is a schematic view of an input coupler comprising a 1×2multimode interference device (MMI).

FIG. 24 is a schematic view of an input coupler comprising a 2×2 MMI.

FIG. 25 is a schematic view of an output coupler comprising a Y-branch.

FIG. 26 is a schematic view of an output coupler comprising adirectional coupler.

FIG. 27 is a schematic view of an output coupler comprising a 1×2 MMI.

FIG. 28 is a schematic view of an output coupler comprising a 2×2 MMI.

DETAILED DESCRIPTION OF THE INVENTION

Mach-Zehnder interferometers have been designed with the two arms of theinterferometer intertwining along adjacent paths with a loopbackstructure that provides for the common heating of adjacent segments ofone arm of the interferometer without interfering with the other arm ofthe interferometer. In some embodiments, the devices involve theincorporation of a more energy efficient thermo-optic phase shifter witha design that simultaneously heats two adjacent portions of a waveguideto capture at least a portion of conducted heat to reduce energyconsumption for a selected phase shift of light passing through thewaveguide. Herein, reference to adjacent waveguide sections includessections of waveguides, such as portions of the same waveguide, whichare laterally adjacent, but are not necessarily longitudinally adjacent.One or both arms of the Mach-Zehnder interferometer can be comprised ofa thermo-optical phase shifter with an energy efficient design. Toprovide for more compact layout of the Mach-Zehnder interferometer whileachieving energy efficiency, a folded pattern is described that involvessimultaneous bending of the two arms of the interferometer in anintertwined configuration while still providing control of the heatingof the individual arms with appropriate waveguide placement. Theloopback design of each arm can open an accessible area suitable for theplacement of the loop of the other arm within an intertwining structure.The Mach-Zehnder interferometers can be integrated into desired planaroptical circuits or packaged along with any additional supportcomponents as a separate device, such as a variable optical attenuator.The design of the Mach-Zehnder interferometer also provides for relativecompact placement within a planar lightwave circuit such that acorresponding device and/or package size is desirably small.

The energy efficient thermo-optic phase shifters within planar opticalwaveguide structures can have a loopback structure to bring two sectionswith opposite light propagation direction for interfacing with a commonheating element to improve heating efficiency while providing for arelatively compact arrangement on the planar structure. Generally, theadjacent heated waveguides are connected by a waveguide loop such thatthe heated sections comprise no more than a selected fraction of thewaveguide area. Such structures provide for particularly effectivethermal efficiencies and relatively small device areas as well asallowing for flexible device designs. In particular, the two arms of theMach-Zehnder interferometer can be placed within a common area withportions of two thermo-optic phase shifters nested in each other in acompact design without significant optical or thermal interferencebetween the arms.

The size and power consumption of a Mach-Zehnder interferometer (MZI) isdetermined, in part, by the selection of material used for thefabrication of the MZI. However, the selection of materials affects manyother aspects of the PLC, including cost of production, cost ofpackaging, and loss associated with optically coupling to the PLC.Various performance factors can be balanced against practical aspectssuch as ability to integrate the components into other devices of theoptical network, cost of the component, which can depend on amount ofmaterials and processing costs and cost of operation. With respect to athermo-optic phase shifter within a fixed selection of materials, aspart of the balance, it can be desirable to reduce the size consistentwith reasonable fabrication costs, which can correspondingly reduceproduction cost and cost of use, as well as power consumption, which canbe a significant cost of use. The difference of index of refractionbetween the waveguide core and the cladding influence the size of theoptical structures while maintaining acceptably low loss frompropagation. In particular, for curved sections of planar waveguides,maintaining an acceptable loss limits the radius of curvature.Correspondingly, the radius of curvature of curved sections ofwaveguides can control the packing of optical devices onto a surface.Thus, the smallest acceptable radius of curvature in some sense providesa distance scale for the placement of optical components in a planarlightwave circuit.

The heater for a thermo-optic phase shifter generally comprises a metalfilm, or other electrically resistive material, over the cladding of anunderlying waveguide core. Typically, electrical contact pads are formedat appropriate locations so that an external circuit may provide avoltage difference across the contact pads thereby causing current toflow though heater. The material and geometry of the contact pad may beconfigured so that it is suitable for using wire bonding as a techniquefor providing electrical contact to external circuitry. Generally, apassivation layer can be deposited over the patterned metal film toprotect the patterned metal film from corrosion while it remains at anelevated temperature during the course of its heating function.Electrical connections to an outside circuit and power source to theheater can be made appropriately through a hole in the passivation orprotective layer. As current flows through the heater, electrical poweris dissipated and converted to heat which increases the temperature ofthe material in the vicinity of the heater, including the opticalwaveguide beneath the heater. By elevating the temperature of thematerial that forms the optical waveguide, the index of refraction ofthe material is changed, which changes the phase delay associated withthe optical propagation through the waveguide; hence the light emergingform the exit of the heated waveguide is shifted in phase relative tothe phase of the light emerging from a similar unheated waveguide. Inthis context, efficiency can be evaluated by the optical phase shiftachieved relative to the electrical power delivered to the heater.

To further satisfy the demand for reduction of component size and ofpower consumption, it can be desirable for MZI devices to havethermo-optic phase shifters that are more efficient with respect toconsumption of electrical power and are either more compact orconfigured to enable more compact MZI designs. The general concepts ofthe compact, energy efficient thermo-optic phase shifters are describedmore completely in a copending and simultaneously filed patentapplication Ser. No. 15/846,755 now U.S. publication US 2018/0173025 toMcGreer et al. (hereinafter the TOPS application), entitled “PlanarOptical Phase Shifters With Efficient Heater Placement,” incorporatedherein by reference. Embodiments of these efficient thermo-optic phaseshifters relevant for the MZI designs described herein are describedseparately below as well as in the context of the MZI structures.

For the energy efficient configurations, the heater is located toprovide heat to two adjacent waveguide sections while not extending toofar relative to the outer edges of the waveguides to reduce lost heatnot contributing to the optical phase shift and to reduce thermalconduction into other regions of the PLC where it may be desirable toplace waveguides that are not intended to be significantly heated, suchas the other MZI arm. In some embodiments, in the plane of thestructure, the heater structure does not extend beyond the outer edgesof the adjacent waveguides. To reduce energy waste from the heater, itis possible to further reduce the heater size while achieving desiredoptical phase shifts and optical performance. The further reduction inheater size can involve further reductions in heater width and/orintroduction of a gap in the heater structure between the adjacentwaveguides. The energy saving can be achieved through the capture ofsome conducted heat that would otherwise be wasted. Further details ofheater embodiments are provided in the context of the figures below.

To effectively capture conducted heat for thermo-optic phase shiftingpurposes, commonly heated adjacent waveguides should be relatively closein the plane of the structure. But the placement of adjacent waveguidescan be limited by distance dependent optical crosstalk between thewaveguides that introduces noise into transmitted optical signals. Dueto natural phase misalignment between adjacent curved waveguides, curvedwaveguides can be placed closer together without exceeding a selectedlimit of optical crosstalk. For these embodiments, the heater also canbe curved to conform the heater shape to the curved waveguide shape inwhich the resulting configuration can provide for desired energyefficiency as well as compact placement of the waveguides. Withwaveguides closer together, the heater can be made correspondinglysmaller, which can be desirable from an overall size perspective, andthermal conduction from the heater can be more effectively captured bythe adjacent waveguides, which can result in further energy savings fromthe operation of the thermo-optic phase shifter. While it can bedesirable for the adjacent waveguide segments to be curved both from athermal efficiency standpoint and a packing standpoint, in someembodiments, the adjacent commonly heated waveguide segments can bestraight or a combination of straight and curved. The discussion in thefollowing focuses on the curved embodiments since these embodimentsprovide advantages especially related to compact placement in the MZI,but embodiments of energy efficient thermo-optic phase shifters withstraight adjacent heated section are described in more detail in theTOPS application. As explained further below, curved heated adjacentwaveguide sections connected with a loop can form an open, accessiblearea suitable for the placement of a loop of the other MZI arm, and viceversa.

In general, MZI incorporating the phase shifters described herein aredesigned for reduced energy consumption, and they may or may not savedevice area relative to a more straightforward design. However, anincrease in device size can be undesirable from the perspective of theuse of additional materials in the fabrication and the need for morespace in the facility maintaining the devices. Thus, to providecommercial value, the devices can balance the energy savings with thevarious costs associated with any increased device size. The improveddevices herein provide desirable packing to provide a smallercorresponding device size while providing good energy savings.Mach-Zehnder interferometers can be used for forming various PLC baseddevices, such as planar optical attenuators and other optical devices,and MZI can effectively incorporate Applicant's energy efficientthermo-optic phase shifter designs for the formation of correspondinglyenergy efficient MZI devices.

A functional schematic diagram of an MZI 100 is shown in FIG. 1. MZI 100comprises an input coupler 102 comprising a first output port 104, asecond output port 106, first input port 108, and optional second inputport 110, which can be dormant or absent; an output coupler 120comprising a first input port 122, a second input port 124, first outputport 126, and optional second output port 128, which can be dormant orabsent; a first waveguide arm 130 optically connecting first output port104 of input coupler 102 to first input port 122 of output coupler 120;and a second waveguide arm 132 optically connecting second output port106 of input coupler 102 to second input port 124 of output coupler 120.As used herein, the “waveguides” and portions thereof are referencedrelative a core optical material, although the optical cladding doesinfluence the transmission of optical signal even though the opticalsignals are concentrated within the core. MZI 100 further comprises afirst phase shifter 140, generally a heater, on first waveguide arm 130and a second phase shifter 142, generally a heater, on second waveguidearm 132. Generally, the corresponding phase shifters can be thenreferred to as thermo-optic phase shifters. In this functionalschematic, the physical location of the BC (B′C′) segment relative tothe DE (D′E′) segment is not intended to be indicated in any way by thedrawing, but in some desirable embodiments shown below, segments BC(B′C′) and DE (D′E′) can be physically arranged close to each in thedevice layout, which can be based on the concepts described in detailherein relating to energy efficient and relatively compact phase shifterdesigns.

An embodiment of an MZI 150, with a corresponding MZI layout schematicshown in FIG. 2, represents the comparable device of FIG. 1 whileschematically showing relative locations of various segments noted withthe corresponding letters on the MZI arm with proportions that aremodified from real proportions to aid in the clarity of the perspective.Referring to FIG. 2, MZI 150 comprises input coupler 152, output coupler154, first MZI arm 156 and second MZI arm 158. A phase shifter/heater160 on first MZI arm 156 can occupy a non-interfering different locationon the PLC than a phase shifter/heater 162 on second MZI arm 158,although an MZI can comprises a single phase shifter/heater in someembodiments. Waveguide loops 164, 166 connected oppositely orientedsections of heated waveguides of first MZI arm 156 and second MZI arm158, respectively.

The respective arms of the MZI have phase shifter designs can be basedon the design of energy efficient phase shifters discussed in moredetail below. In particular, FIG. 3 describes an optical phase shifterembodiment with curved heated sections similar to each of the two phaseshifters of FIG. 2 along with a heater that has a projection in theplane of the waveguide that is also curved. With an energy conservingMZI embodiment of a phase shifter used in the MZI of FIG. 2, the area ofthe PLC occupied by the pair of spatially separated MZI arms with phaseshifters, is approximately twice the area occupied by an individual MZIarm with their respective phase shifters. Reducing this size-doublingfootprint associated with the inclusion of the second phase shifter isan objective of additional compact MZI embodiments described herein.

An embodiment of a phase shifter 200 with curved heated sections isdepicted in a schematic top view in FIG. 3. Phase shifter 200 comprisesa heater 201, and an optical waveguide 202. Waveguide 202 comprises afirst curved heated waveguide section 203 (situated between point B andpoint C), a second curved heated waveguide section 204 (situated betweenpoint D and point E), a loopback optical waveguide section 205 (situatedbetween point C and point D) that optically connects the first andsecond curved heated waveguide sections, a first connecting waveguidesection 206 optically connected to first curved heated waveguide section203 and second connecting waveguide section 207 optically connected tosecond curved heated waveguide section 204. Loopback optical waveguidesection 205 has a loop marked with points S and T, which are describedfurther below. The letters A-F are selected to orient phase shifter 200relative to the MZI structure of FIG. 2, although end points A and F areshown arbitrarily ending in FIG. 3 even though in a device thewaveguides generally would be connected appropriately within the PLCbased on an overall design for the PLC.

Consistent with this configuration, second curved heated waveguidesection 204 has a smaller average radius of curvature relative to firstcurved heated waveguide section 203. The average radius of curvature ofloop S-T is smaller than the average radius of curvature of B-C. WhileFIG. 3 shows loop S-T with a semicircular structure and C-S mostlystraight, these conditions can be relaxed, and for the relaxedconfigurations, the point S can be selected at the point at which theradius of curvature becomes smaller than the average radius of curvatureof section B-C. Heater 201 provides a thermal region 208 so that theaverage temperature within the thermal region is higher than theneighboring region 209 located in the plane of the structure outside ofthermal region 208. First curved heated waveguide section 203 and secondcurved heated waveguide section 204 are within the thermal region 208,and loopback optical waveguide section 205 is within neighboring region209. Portions of the waveguide 202 that are significantly heated are theportions that are within the thermal region 208, which extends beyondheater 201 area due to thermal conduction. Portions of the waveguide 202that are within the neighboring region 209 can be considered as unheatedor not significantly heated.

In the context of the view in FIG. 3, heater 201 is not intended to havea particular specific relationship with respect to heated waveguidesections 203, 204, in particular with respect to extent on the plane ofthe structure. Various representative embodiments of the heater withrespect to extent on the plane of the device are shown in FIGS. 4-8,which are described further below. Additional specific heaterembodiments can be found in the TOPS application, although the ranges ofsuitable heater structures are commensurate, and in some embodimentsbroader, herein.

In the embodiment of FIG. 3, the optical waveguide 202 can be describedin convenient notation by describing the nominal physical path of theoptical waveguide as a parametric curve using “t” as the parameter ofthe curve, where t=0 at point A and t=1 at point F, each of which areillustrated in FIG. 3. When assembling this phase shifter into a MZI,the waveguide can be further extended from point F, and point A can beconnected to a splitter/coupler, as described further below withalternative and additional parameterization of the nominal physical pathin the same spirit as shown in FIG. 3. The nominal physical pathgenerally is distinguished from the specific physical path in an actualdevice because the nominal physical path does not include sub-wavelengthperturbations such as waveguide offsets at the transitions betweenstraight waveguide and curved waveguides that is a common practice inthe art and possibly other similar design details. For conventionherein, the signed curvature is negative at any point P along the curvewherein an increasing value of parameter t causes a clockwise trajectoryin the plane. Correspondingly, the signed curvature is positive at anypoint P along the curve wherein an increasing value of parameter tcauses a counterclockwise trajectory in the plane. The signed curvatureis zero at any point P along the curve wherein an increasing value ofparameter t causes a linear trajectory. For the purposed herein for anywaveguide segment at an arbitrary location with a length along the lightpath of 10 microns or more, a linear trajectory can be associated withany waveguide segment with a radius of curvature of at least amillimeter, and any segment with a radius of curvature less than amillimeter is considered curved. Similarly, a heating element placed toconform to one or two curved waveguide segments can be considered acurved heater through examination of the contours of the heating elementin the plane of the waveguides.

As illustrated in FIG. 3, the first curved heated waveguide section 203has a signed curvature that has a constant value that is negative alongthe entire length of the section, and the second curved heated waveguidesection 204 has a signed curvature that has a constant value that ispositive along the entire length of the section. Correspondingly, curvedheated waveguide sections 203 and 204 have opposite optical propagationdirections resulting from the curvature of loopback optical waveguidesection 205. However, other embodiments are anticipated for which thefirst curved heated waveguide section 203 has a signed curvature thatvaries along the segment length and may even have points along thesegment for which the signed curvature is zero in value. For example,the first curved heated waveguide section may follow a spline curve,wherein the radius of curvature continuously varies or intermittentlyvaries along the length of the curved heated waveguide or,alternatively, may have one or more linear segments alternating withnonlinear segments. Likewise, other embodiments are contemplated forwhich the second curved heated waveguide section 204 has a signedcurvature that varies along the segment length and may even have pointsalong the segment for which the signed curvature is zero in value. Forthese embodiment, an average radius of curvature can be considered forthese sections. However, embodiments for which the first curved heatedwaveguide section 203 has a signed curvature of zero along its entirelength (that is embodiments for which the first curved heated waveguidesection is a linear section) does not take advantage of the opportunityto achieve a desired compact configuration. Likewise, embodiments forwhich the second curved heated waveguide section 204 has a signedcurvature of zero along its entire length (that is embodiments for whichthe second heated waveguide section is a linear section) does not takeadvantage of the opportunity to achieve a desirably compactconfiguration. FIG. 3 depicts an embodiment that achieves desirablecompactness by configuring the first curved heated waveguide section 203and the second curved heated waveguide section 204 with signed curvaturevalues that have similar magnitudes and opposite signs. Additionaldetails related to the values of the signed curvature that can achievecompactness and efficiency are described below.

Three waveguide segments are marked along loopback optical waveguidesection 205 (points C-D) in FIG. 3. Point T marks a transition pointwhere the curvature along the parameterized waveguide changes frompositive to negative, and point S marks a transition point from a highlycurved loop segment (S-T) 221 to a straight or slightly curved segmentalong loop section (C-S), extension segment 220, that provides for acompact configuration. Extension segment 220 (points C-S) connects firstcurved heated section 203 with a loop segment 221. Thus, loopbackoptical waveguide section 205 can be considered to comprise extensionsegment 220 (segment C-S), loop segment 221 (segment S-T) and connectionsegment 222 (segment T-D). A shown in the FIG. 3, most of the segmentC-S is straight, but C-S can have some curvature as long as otherconstraints are achieved, such as the radius of curvatures of T-D andS-T do not fall below the selected cut off value to avoid undesirableoptical loss. Also, extension segment 220 (C-S) can comprise a curvedportion near point C depending on the position of heater 201 since pointC is positioned based on thermal region 208 and not by curvature. Inthis embodiment, the average radius of curvature of loop S-T is smallerthan the average radius of curvature of B-C. While FIG. 3 shows loop S-Twith a semicircular structure and C-S mostly straight, these conditionscan be relaxed, and for the relaxed configurations, the point S can beselected at the point at which the radius of curvature becomes smallerthan the average radius of curvature of segment B-C.

The use of adjacent heated waveguide sections provide for heaterplacement that can reduce power consumption to operate the phaseshifter. Generally, reducing the separation between the waveguidesections within the thermal region increases the efficiency because itplaces both waveguides closer to the hottest section of the thermalregion. However, reducing the separation between the waveguidesgenerally increases the optical crosstalk between the waveguides, whichcan degrade the performance of the device through the introduction ofnoise in the optical signal carried in the waveguide. Generally, thewaveguide sections are placed far enough apart to obtain acceptable lowlevels of crosstalk/noise. Hence the waveguide separation and,consequently the efficiency, is limited by the minimum waveguideseparation permitted by the acceptable limit for optical crosstalk. Fora fixed waveguide separation, the embodiment depicted in FIG. 3, reducesthe optical crosstalk relative to an embodiment with adjacent linearwaveguide by breaking the phase matching condition due to the curvature.Light that propagates through one straight waveguide stays in phase withlight that propagates through a second straight waveguide that isequivalent in design and parallel with the first waveguide. In otherwords, the phase matching condition will be maintained for two waveguidethat are equivalent, straight and parallel.

When the phase matching condition is maintained, optical crosstalk isgreater all else being equal. Light that propagates through one curvedwaveguide will not stay in phase with light that propagates through asecond curved waveguide that is equivalent in design and adjacent withthe first waveguide. Specifically, if the adjacent waveguide sectionsare curved, the difference in radius of curvature results in phasemisalignment as the signals transmit through the adjacent waveguidesections that naturally reduces the optical coupling leading tocrosstalk. In other words, light that propagates through one curvedwaveguide section does not stay in phase with light that propagatesthrough a second curved waveguide section and adjacent with the firstwaveguide section. Thus, the phase matching condition is not maintainedfor two waveguide that are equivalent apart from position, curved andadjacent. When the phase matching condition is broken, for a fixedwaveguide separation, optical crosstalk is reduced. Thus, due to thereduced crosstalk at an equivalent spacing of adjacent waveguidesections, adjacent curved waveguide sections can be placed closer toeach other with acceptable crosstalk/noise of a transmitted signal. Thecombination of the curved heated waveguide sections and the heaterplacements described herein provide for particularly efficient designs.

By using curved heated waveguides, as depicted in FIG. 3, for a givenlimit on optical crosstalk, the waveguide separation can be reduced. Byconfiguring the waveguides with reduced separation, the embodimentdepicted in FIG. 3 can have improved thermal efficiency. Furthermore,improved efficiency can be achieved by configuring the separation, sA(noted in FIGS. 4-8), between first curved heated waveguide section 203and the second curved heated waveguide section 204 to have a constantvalue that is the smallest value determined by the selected opticalcrosstalk restriction. This configuration can be achieved by configuringthe first curved heated waveguide section 203 and the second curvedheated waveguide section 204 to lie along arcs of mutually concentriccircles wherein the radius of the two circles differs by a value equalto waveguide separation allowed by the selected optical crosstalkrestriction. Our experimental measurements with similar devicesdemonstrate that substantial heater efficiency improvement when sA has avalue of 20 microns or less with a configuration depicted schematicallyin FIG. 3 in commercial grade silica glass planar lightwave circuits.Additional details related to the values of the signed curvature thatcan provide desirable compactness and efficiency are described below.

The positioning of the heater to simultaneously heat two adjacentwaveguide sections can provide desirable energy saving since thermalconduction can be captured at least in part. The design of the heaterconfiguration can be influenced by a range of parameters including, forexample, materials of the components, layout, performance criteria,nature of the signals to be transmitted, etc. Representativeconfigurations in a cross sectional view along line A-A of FIG. 3 areshown in FIGS. 4-8. For convenience, the basic structure in FIGS. 4-8 isreferenced to the same structural features in FIG. 3 with focus on thechanging of the heater. In the plane of the waveguides, the heaterprojection generally is curved mimicking the curvature of the heatedwaveguide sections. Thus, the projection of the heater in the waveguideplane has a length, width and curvature. Generally, the radius ofcurvature of the heater projection along the center of the width of theprojection can be approximately the average of the radii of curvature ofthe adjacent two curved heated waveguide sections.

With a particular placement of a heater, a corresponding thermal zone(or, equivalently, heated zone) can be expected within which thewaveguide is significantly heated. The thermal zone extends beyond theheater position due to thermal conduction. References to points andfeatures relative to the thermal zone, are understood to refer to thelocation in the plane of the device unless explicitly indicatedotherwise. The hot point refers to a point or region on the plane of thedevice with the highest temperature within measurement error. The heatdissipates gradually, but the boundary of the thermal zone can bespecified for convenience where the temperature increase from ambient isa factor of two less than the temperature increase over ambient due tothe heater at the hot point. As noted below, the edge of the thermalzone specified this way approximately indicates the region in whichheating of the waveguide sections can result in energy efficiencyrelative to a traditional design. In embodiments of particular interest,the thermal zone extends across the width of the waveguides whether ornot the heater element extends across the width of the waveguides. Butthe thermal zone generally does not extend too far past the edges of thewaveguides to reduce the wasted thermal energy, so the heater isgenerally shaped to have a projection in the plane of the waveguidesmimicking the shape of the heated waveguide sections, which can becurved for the several advantageous reasons described herein. Furtherdiscussion of the thermal contours is found in the co-filed TOPSapplication. Due to the thermal conduction, heating between the adjacentwaveguides tends to provide heat to both waveguides, so placement of theheater completely or with significant portions between the waveguidescan provide efficient energy use.

Referring to a sectional view in FIG. 4, phase shifter 200 (FIG. 3)comprises an optional substrate 230, cladding 231 surrounding heatedwaveguide sections 203, 204, and optical overcoat 232 covering heater233. As noted above, references to waveguides and waveguide sections arereferenced to the core optical material that carries most of the opticalsignal. As shown in FIG. 4, heater 233 has a width wH larger than theseparation between adjacent heated waveguide sA, which is shown as acenter to center distance. In this embodiment, with reference to theplane of the device, outer edges 234, 235 of heater 233 extend pastouter edges 236, 237 of heated curved waveguide sections 203, 204,respectively, while heater 233 also extends over the space betweenheated waveguide sections 203, 204. Thermal zone 238 is shown in FIG. 4extending in the plane beyond outer edges 234, 235 of heater 233 due tothermal conduction. The dashed lines marking thermal zone 238 aredepicted in FIG. 4 as vertical, although thermal conduction from heater233 would not generally be expected to follow such a configuration.However, the thermal conditions at the level within the structure of theheated waveguides is the significant reference position, so the markingsof the thermal zone generally herein can be considered to be at thisrelevant depth within the structure. It has been discovered that furtherthermal efficiency can be achieved through a reduction of the heaterwidth across the heated waveguides while maintaining desirable opticalproperties and control of the thermo-optic phase shift.

In use, heat from heater 233 is conducted into the waveguide cladding231 and subsequently conducted into heated waveguide sections 203, 204.The elevated temperature of first heated waveguide section 203introduces a phase shift onto the light that propagates through thefirst curved heated waveguide section relative to correspondingpropagation at ambient temperature. Similarly, the elevated temperatureof second curved heated waveguide section 204 introduces a phase shiftonto the light that propagates through the second curved heatedwaveguide section relative to propagation at ambient temperature.Because loopback optical waveguide section 205 optically connects heatedwaveguide sections 203, 204, light that propagates through first curvedheated waveguide section 203 also propagates through second curvedheated waveguide section 204 and consequently, the phase shiftsintroduced within the active waveguide sections combine to produce a netphase shift that is approximately the sum of the two individual phaseshifts. Hence, by situating first curved heated waveguide section 203and second curved heated waveguide section 204 in close proximity, thedevice can use the indirect heating contribution to make the phaseshifter more energy efficient. Smaller separation between the firstwaveguide section and the second waveguide (that is, smaller sA values)can yield greater energy efficiency of the phase shifter within opticalperformance constraints. In particular, as shown in FIG. 3 as well as inMZI embodiments described below, the optical waveguide passes throughthe thermal zone twice, once where a first curved heated waveguidesection is within the thermal zone and a second instance where a secondcurved heated waveguide section is within the thermal zone. Because theoptical waveguide passes through the thermal zone twice, the opticalphase shift caused by a fixed electrical power applied to the heater isapproximately double the value relative to the optical phase shiftcaused by an equivalent design (e.g., a design with equivalent heaterand waveguide dimensions and relative positions) where the opticalwaveguide passes through the thermal region only once. Hence, phaseshifter embodiments described herein can exhibit roughly double theefficiency relative to a similar design where the optical waveguidepasses through the thermal region only once. Correspondingly, thethermal zone in the plane of the waveguides can have a boundary wherethe temperature increase over background drops to one half of thehighest temperature increase over background (hot point) in the plane.

Representative heater configurations with reduced heater widths areshown in FIGS. 5-8. FIGS. 5-8 depict heater embodiments that arepositioned with respect to the corresponding waveguide sections in anapproximately symmetrical fashion to heat the two waveguide roughlyequally, although such symmetrical configurations may not be needed toachieve desirable energy efficiencies and asymmetrical configurationsare contemplated. With respect to a more energy efficient heaterconfiguration, FIG. 5 depicts a heater extending in the plane from theouter edges of heated waveguide sections 203, 204 spanning the regionbetween the waveguides. FIGS. 6-7 depict heaters that are sequentiallysmaller while spanning the center of the space between the heatedwaveguide sections, and FIG. 8 depicts the splitting of the heater intotwo heater elements with a gap in the heater in the space between theheated waveguide sections. These embodiments are next discussed in moredetail.

Referring to FIG. 5, heater 250 has a width in the plane of the devicewith outer edges 251, 252 approximately aligned with the outer edges236, 237 of heated waveguide sections 203, 204. Thermal zone 253 isshown to be somewhat smaller than thermal zone 238 of FIG. 4. A centerline is drawn in the heater just for visualization purposes. FIG. 5shows the spacing between the centers of heated waveguide sections 203,204 as sA. The relationships relating to the heater width can beexpressed as sH=sA+wa+wb, where wa and wb are half widths of therespective heated waveguide sections.

Referring to FIG. 6, heater 260 is positioned with outer edges thatoverlap with heated waveguide sections 203, 204 in the plane of thestructure. Outer edges 261, 262 of heater 260 are positioned toward thecenter relative to the outer edges 236, 237 of heated waveguide sections203, 204. Thermal zone 263 extends laterally somewhat less than thermalzone 253 of FIG. 5. In this approximately symmetric structure,sA−wa−wb<sH<sA+wa+wb. In an additional heater embodiment (see figure inTOPS application), sH=sA−wa−wb, or in other words, the outer edges ofthe heater in the plane are approximately aligned with the inner edgesof heated waveguide sections 203, 204. FIG. 7 depicts a heaterembodiment in which the width of heater 266 is less than the widthbetween heated waveguide sections 203, 204. Thus, in the plane of thestructure, heater 266 is between curved heated waveguide sections 203,204 with outer edges 267, 268 within inner edges of heated waveguidesections 203, 204, and heater 266 does not overlap the waveguides alongthe plane. So for the heater embodiment in FIG. 7, sH<sA−wa−wb. Thermalzone 269 is depicted as being correspondingly somewhat smaller. Theheaters in FIGS. 5-7 are depicted below optional overcoat 232 and on topof cladding 231, which is shown on optional substrate 230. TogetherFIGS. 5-7 depict various widths of the heater that represent possibleconfigurations from sH=sA+wa+wb to sH<sA−wa−wb. Additional embodimentsof heater widths include other values of sH<sA+wa+wb in addition to thedepicted configurations, and the design selection of the specific valuescan depend on the range of additional details summarized generallyherein. In a commercial device design, various considerations can enterinto a design selection including optical performance, layout in thePLC, energy efficiency, materials, processing considerations, and otherspecific performance issues. Some ranges of suitable values for silicabased optical devices are provided below.

The effective shrinking of the heater width (and generally area)relative to the embodiment of FIG. 5 through the division into twoheater elements is depicted in FIG. 8. Referring to FIG. 8, a heater 270is parsed into heater elements 271, 272 with a gap 273 separating theheater elements on the surface of optional overcoat 232. In thisembodiment, outer edge 274 of heater element 271 is positioned overfirst heated waveguide section 203 in the plane of the structure, andouter edge 275 of heater element 272 is positioned over second heatedwaveguide section 204. Gap 273 represents a decrease in the area ofheater 270 relative to a corresponding heater without the gap separatingthe heater into two heater elements. A corresponding thermal zone 276 isnoted in FIG. 8. The introduction of gap 273 generally changes thethermal distribution of the device in use with the expectation of somethermal conduction from heater element 271 to second heated waveguidesection 204 and from heater element 272 to first heated waveguidesection 203, which can contribute to the energy efficiencies of thethermo-optic phase shifter.

FIG. 8 displays a heater embodiment that reduces the width of heatermaterial across the plane of the structure perpendicular to the opticalpath defined by the waveguide at least in part through the introductionof a center gap between two heater elements. This embodiment of theheater can provide alternative thermal distributions relative to theheater embodiments in FIGS. 5-7 that also reduce their widths relativeto the heater embodiment in FIG. 4. In addition to the embodiment ofFIG. 8, the size of the gap can be adjusted, and the outer edges of theheater elements can be selected to achieve desired thermal responsewhile achieving desirable reduction of energy use. In general, theselection of a particular design can depend on various designparameters, optical performance, expectation of operation conditions,processing considerations and potentially additional factors. Generally,selected designs can provide efficient thermal operation for thethermo-optic phase shifter.

FIG. 9 is a schematic top view of a thermo-optic phase shifter 280 witha configuration of electrical interconnects to power a heater 281 with athermal zone 282 depicted such as may be used for the embodiments inFIGS. 4-7 discussed above. For convenience the optical components areassociated with the corresponding optical components of the generalphase shifter of FIG. 3, which are also used for FIGS. 4-7. As shown, ator near each end of heater 281 is connected with electrical connections283, 284 to respective terminals of a voltage source 285, which isconnected to controller 286. Other arrangements of electricalconnections are possible as will be readily recognized by a person ofordinary skill in the art. In one such alternative embodiment, aconnection near the center of heater 281 is connected to one pole of apower source while connected at or near the ends of heater 281 areconnected to the other pole of the power source. Controller 286 for thisembodiment and all other embodiments described herein can be a digitalprocessor or the like, and can be considered present whether or notshown in a specific figure. In additional or alternative embodiments,the heater or heaters can be segmented along the length of the adjacentwaveguide sections. Such an embodiment of the thermo-optic phase shifteris depicted in FIG. 10 again with the optical components, i.e.,waveguide, of FIG. 3. FIG. 10 is a schematic top view of a phase shifter290 with two heater elements 291, 292 separated on the arc of firstcurved heated waveguide section 203 and second curved heated waveguidesection 204 and with a configuration of electrical interconnects topower heater elements 291, 292. Heater elements 291, 292 providecorresponding thermal zones 293, 294. This configuration of heaterelements divides first heated optical waveguide section 203 into a firstheated segment, a second heated segment and connecting segment, andsimilarly second curved heated waveguide section 204 into first heatedsegment, a second heated segment, and a connecting segment. The firstheated segments of first curved heated waveguide section 203 and secondcurved heated waveguide section 204 are within first thermal zone 293,and the second heated segments of first curved heated waveguide section203 and second curved heated waveguide section 204 are within secondthermal zone 294.

Referring to FIG. 10, outside ends of heater elements 291, 292 areconnected to the positive side of a voltage source 295 respectively withconnections 296, 297, and inside ends of heater elements 291, 292 areconnected to negative side of voltage source 295, respectively, withconnections 298, 299. In this configuration, a gap is introduced intothe heater at a location midway between the ends. Electrical connectionis completed for both heater segments by providing electrical connectionfrom the negative terminal of the voltage source to the heater elementsat or near each side of the electrically isolating gap. In onealternative configuration, a separate and independent voltage sourcecould be used for each heater element. A wide variety of other divisionsof the heater and reasonable arrangements of heater segments will beapparent to those practiced in the art based on the teachings herein.

FIG. 11 shows a schematic top view of a phase shifter with electricalconnections for a heater with two heater elements separated from eachother along the width relative to two adjacent waveguide sections, suchas those shown in the sectional view of FIG. 8. Similar electricalconnections can be used for other similar embodiments of the phaseshifter. Referring to FIG. 11, thermo-optic phase shifter 310 is againdepicted on the optical waveguide platform of FIG. 3 for convenience.The heater for phase shifter 310 has heater elements 311, 312 thatprovide a thermal zone 313 that covers first curved heated waveguidesection 203, second curved heated waveguide section 204 and heaterelements 311, 312. As shown, each heater element 311, 312 isindependently connected to a common voltage source 314 throughconnections 315 and 316 to heater element 311 and connections 317, 318to heater element 312. Other arrangements are possible as will berecognized by a person of ordinary skill in the art based on theteachings herein. In one alternative configuration, a separate andindependent voltage source could be used for each heater element. In asecond alternative configuration, the heaters may be electricallyconnected to each other at each end such that the electrical connectionsthat join the heaters are integrated within the PLC. Heater elementsdivided along their width as shown in FIGS. 8 and 11 can also be furtherdivided along the arc as shown in FIG. 10, with heater elements of FIG.8 or 11 divided along the arc for each waveguide, that wouldcorrespondingly result in four heater elements with further divisionsalong the arc possible. While the terminology is used in which heaterelements associated with one phase shifter are collectively referred toas a single heater, it will be recognized that this is merely semantics,and that one or groups of heater elements can be effectively separateheaters with separate control of current flow to generate heat from theparticular elements.

A variable voltage source is depicted in FIGS. 9-11 as the source ofelectrical power used to drive the heaters; however, those practiced inthe art will understand that a variety of other options are possible,including but not limited to a variable current source and a pulse widthmodulation circuit.

In general, the separation, sA, between adjacent points of the activewaveguides may vary along the length of the device; however, in someembodiments, sA maintains an approximately constant value along thedevice. As described above, if the waveguides approach too closely,optical performance can suffer, and if the waveguides separate too far,thermal efficiencies can be reduced. For example, with curved heatedwaveguide sections, the first heated waveguide section may be aligned tothe arc of a circle with radius R₁ and centered at point P, while thesecond heated waveguide section may be aligned to the arc of a circlewith radius R₂ and centered at point P and R₁ is greater than R₂ by avalue that is equal to sA. In this example, R₂ can be selected to have avalue that is large enough to prevent substantial bend loss (that is,the loss associated with light propagating around a bend). For example,for a waveguide that comprises a channel waveguide with a 1.8% indexcontrast, a typical application may require that R₂ be greater or equalto about 1 mm. Of course, in the structure of FIG. 3, the average radiusR_(L) of loop segment 221 is smaller than the radius R₂, so that thebend loss concern can be appropriately referenced to R_(L).

While the structure in the previous paragraph may be a particularlydesirable design, reasonable performance can be achieved with arelaxation of these conditions, such as having somewhat non-circularwaveguide segments. Also, the spacing sA may not be approximatelyconstant, but can range from the average sA±20% of the average. A personor ordinary skill in the art will recognize that additional rangeswithin the present ranges are contemplated and are within the presentdisclosure. If sA is referenced without further comment, sA refers tothe average value.

The selection of the value of sA can avoid undesirable optical couplingof the active waveguides if they are situated sufficiently close toeach, that is, if sA is undesirably small. Substantial optical couplingcan result in undesired optical performance. Herein, sW refers to aselected cut off value (lowest value) for the center to center waveguideseparation, sA, above which sufficiently small optical coupling betweenwaveguides provides acceptable optical performance. The selection of thevalue of sW depends on the details of the waveguide construction, on thedetails of the values of the index of refraction of the variousmaterials that are used, and on the tolerance of the consideredapplication towards the performance degradation related to opticalcoupling between optical waveguides. Furthermore, one of ordinary skillin the art will be able to select the value of sW, either fromexperience, experimental measurements and/or by numerical simulations,applicable for their intended application and for the optical waveguidesfor the particular application.

Consequently, in some embodiments, the value of sA can be selected to beapproximately the smallest value consistent with selected restrictionsassociated within fabrication limits and with spatial selected cutoffspacing on acceptable optical coupling. The selection of the smallestvalue of sA for desired performance depends on the details of thewaveguide construction, on the details of the values of the index ofrefraction of the various materials that are used, and on the toleranceof the considered application towards the performance degradationrelated to optical coupling between optical waveguides, which in someembodiments can be selected to be no more than about −27 dB. As known inthe art, efficient optical coupling between adjacent waveguides requiresmodes of the respective waveguides to remain in phase with each other asthey propagate; i.e., efficient coupling involves the phase matchingcondition to be satisfied. Adjacent curved waveguides with equal widthsdo not satisfy the phase matching condition, hence, the curved waveguidedepicted in FIG. 3 exhibits less efficient optical coupling thanstraight waveguide for the same value of sA, which is a desirablefeature of the curved waveguides. Consequently, the waveguideconfiguration with curved waveguides allows for a smaller value of sAand consequently allows for improved phase shifting energy efficiencyrelative to an embodiment straight commonly heated waveguide sections.Our experimental measurements on the thermo-optic phase shifter similarto FIG. 3 having channel waveguides with a 1.8% index contrast relativeto the cladding material indicates that straight waveguide sections maybe situated such that sA has a value of at least about 12 microns toavoid substantial performance degradation associated with opticalcoupling and curved waveguide sections may be situated such that sA hasa value of at least about 10 microns to avoid substantial performancedegradation, although smaller separations may still provide performancedegradation within an acceptable range for many applications. Ourexperimental measurements with similar devices suggest that substantialheater efficiency improvement are expected when sA has a value ofroughly 30 microns or less. Consequently, desirable results can beobtained with waveguide with 1.8% index contrast has sA with the rangefrom 10 microns to 30 microns and in further embodiments from about 10microns to about 25 microns. A person of ordinary skill in the art willrecognize that additional ranges of sA within the explicit ranges arecontemplated and are in the present disclosure. Phase shifters wereformed with silica glass with a 1.8% index of refraction difference withseveral values of sA as well as a traditional design. The traditionaldesign exhibited an energy efficiency of 0.62 degrees/mW. Two differentvalues of sA (20 microns or 12 microns) were used to obtain energyefficiencies of was 0.98 degrees/mW or 1.12 degrees/mW, respectively,corresponding to efficiency improvements of 1.58 or 1.81. Avoidance ofoptical coupling between adjacent waveguides restricts the efficiencyimprovement to be less than the factor of 2 theoretical limit.Furthermore, the curved heated waveguide sections of the inventivethermo-optic phase shifter reduce the footprint of the device allowingfor more compact implementations.

An attempt to capture some lost heat to form a more energy efficientthermo-optic phase shifters for an MZI is described in U.S. Pat. No.8,103,136 to Chen et al. (hereinafter Chen), entitled “Thermo-OpticDevices Providing Thermal Recirculation,” incorporated herein byreference. Referring to FIG. 12, an MZI 340 is shown that correspondsroughly to FIG. 5 of Chen. MZI 340 comprises directional couplers 341,342, waveguide arms 343, 344, and two thermo-optic devices 345, 346.Each waveguide arm 343, 344 have two loopback sections to form foldedoptical paths with several laterally displaced waveguide sectionsassociated with each thermo-optic device 345, 346. Chen does notrecognize the significant efficiencies with respect to layout and energyuse from using curved commonly heated adjacent waveguide sections asshown in FIG. 3 herein, or the improved placement of the heaters, suchas shown in FIGS. 5-8 herein, or the significant size advantages fromintertwining the two MZI arms. The intertwining of the MZI arms isdiscussed in the following.

While the MZI layout in FIG. 2 provides a relatively compact structurefor each MZI arm with reduced energy use through thermal efficiencies,each arm necessarily occupies a significant area due to constraintsnecessitated by the radius of curvature of the waveguide and the overalldevice is roughly twice the size of the two thermo-optic phase shifters.It has been discovered that the geometry of the overall structure of aphase shifter in FIG. 3 can be adapted for overlapping of the areasoccupied by each MZI arm in a partially reciprocally nested(intertwined) configuration so that the entire MZI structure can adoptthe energy conserving structure of the MZI arms with significantly lessthan double the area occupied by each MZI arm. The corresponding layoutof each arm schematic, without intertwining but allowing intertwining,shown in FIG. 13, while schematically showing relative locations ofvarious segments with proportions that are modified from realproportions to aid in the clarity of the perspective.

Referring to FIG. 13, MZI 350 comprises input coupler 351, outputcoupler 352, first MZI arm 353, second MZI arm 354, a first phaseshifter/heater 355 on first MZI arm 353 and an optional second phaseshifter/heater 356 on second MZI arm 354. Waveguide loops 357, 358connected oppositely oriented sections of heated waveguides of first MZIarm 353 and second MZI arm 354, respectively. In a comparison of thephase shifters of FIG. 13 with those of FIGS. 2 and 3, the curvaturesare reversed relative to the waveguides connecting with an adjacentcouple/splitter which then flips the heater position relative to theconfiguration in FIG. 2. These changes in layout result in an open,accessible interior space marked with hashed lines in FIG. 13. The openinterior space provides for the placement of a portion of the other MZIarm within this space for a nested layout, and vice versa. Thecorresponding intertwined layout based on the MZI in FIG. 13 isdescribed in detail below, and in the intertwined layout, the two MZIarms occupy a space significantly smaller than twice the space of asingle MZI arm. This conceptual framework of folding an MZI arm tosimultaneously take advantage of heater placement to heat two adjacentwaveguide arms and forming an open accessible space that can beeffectively used for other waveguides is completely absent from Chen,which maintains distinct areas in the plane of the device for eachwaveguide arm.

The nominal physical paths of the waveguides in FIG. 13 areparameterized with letters similar to FIG. 3 with the addition ofsegments F-G and differences in the structure can be referenced to thesepoints. A comparison of the parameterization can further clarify somedistinctions. Segments A-B (A′-B′) are qualitatively equivalent betweenthe two embodiments. However, the sign of the curvature of B-C isopposite to the sign of the curvature of B′-C′. Likewise, the sign ofthe curvature of C-D is opposite to the sign of the curvature of C′-D′and the sign of the curvature of D-E is opposite to the sign of thecurvature of D′-E′. These changes in curvature result in point F (F′)not being particularly close to connecting with the correspondingcoupler. In the intertwining configurations below, this relativeplacement of structural element is ameliorated to some degree by movingthe couplers out of a linear configuration, which (linear configuration)may be suitable for a conventional MZI design but not necessarilydesirable for the improved designs herein. In FIG. 13, F-G (F′-G′)corresponds with a spiraling waveguide that provides for connection ofthe waveguide from point F (F′) to the respective coupler. Movement ofthe couplers away from the linear configuration is also significant forconsistency with the formation of the intertwined structure. Referringto FIG. 13, the two arms can be superimposed with the loop of one armfitting into the open area adjacent the curved heated sections of theother arm. The portions of the waveguide arms connecting to therespective couplers are moved out of each other's way.

The intertwined configuration is discussed in detail in the following.First, a few additional observations can be useful. Referring to FIG. 3,with a linear waveguide extension from point F, the smallest distancebetween such a linear extension and loop segment 221 measured waveguidecenter to waveguide center is R₂−R_(L)−sA. This distance is used in theentwined structure to open the interior space for the placement of aloop portion of the other waveguide arm.

Referring to FIG. 14, an MZI is shown with intertwined arms, and aparameterized version of the waveguides is discussed with more detailsin the context of FIG. 15 following a more general discussion of FIG.14. As shown in the layout schematic of FIG. 14, MZI 400 comprises afirst MZI arm 401 with a phase shifter that occupies substantially thesame overall location on the PLC as a second MZI arm 402 with a phaseshifter. MZI 400 further comprises optical coupler/splitter (inputcoupler) 403, optical coupler/splitter (output coupler) 404, opticalinputs 405, optionally 406 and optical outputs 407, optionally 408.First MZI arm 401 referencing broad divisions (further refinementdescribed with respect to FIG. 15) comprises outer arc 420, waveguideextension 421, inner heated arc 422, loopback waveguide section 423,outer heated arc 424, connector 425 and heater 426. Similarly, secondMZI arm 402 referencing broader divisions (further refinement describedwith respect to FIG. 15) comprises outer arc 430, waveguide extension431, inner heated arc 432, loopback waveguide section 433, outer heatedarc 434, connector 435 and heater 436.

Relative to the structures of the phase shifters in FIG. 3, MZI arms401, 402 in FIG. 14 have the extra outer arcs 420, 430 that provide forthe two MZI arms to be rolled together in the compact configuration inFIG. 14 with the lateral shift of the coupler/splitters. With thisconfiguration, the area of the resulting PLC occupied by the pair isphase shifters, is roughly the same area occupied by an individual phaseshifter. The reductions in size with the intertwined MZI arms can beparticularly advantageous for material systems requiring a bendingradius that is larger than 500 microns, such as material systems with anindex of refraction contrast below 3%, although the proportionalreduction is significant for any material system. Thus, the MZI designin FIG. 14 can achieve desirable energy efficiencies along withsignificant device size reduction relative to non-intertwining designs.

An extensive parameterization of each waveguide of the MZI in FIG. 14 isdepicted in FIG. 15. Letters A-S (A′-S′ for other waveguide arm) markthe position along the waveguide from one end to the other. MZI 400comprises input coupler 403 having at least one input port A(405), afirst output port B, and a second output port R′. Input coupler 403 maybe a Y-branch splitter, described further below, having only one inputport A and having two output ports B and R′. Alternatively, inputcoupler 403 may be a 2×2 coupler having two input ports A and S′ andhaving output ports B and R′, as shown in FIG. 15. MZI 400 comprisesoutput coupler 404 having at least one output port A′ and having twoinput ports B′ and R. Output coupler 404 may be a Y-branch combinerhaving only one output port A′ and having two input ports B′ and R.Alternatively, output coupler 404 may be a 2×2 coupler having two outputports A′ and S and having two input ports B′ and R, as shown in FIG. 15.

MZI 400 further comprises a first arm 401 comprising a waveguide BR thatoptically couples first output port B of input coupler 403 to the firstinput port R of output coupler 404. The optical waveguide denoted as BRcan be equivalently denoted as RB. MZI 400 further comprises a secondarm 402 comprising waveguide R′B′ that optically couples first outputport R′ of input coupler 403 to the second input port B′ of outputcoupler 404. The optical waveguide denoted by R′B′ may be equivalentlydenoted as B′R′. MZI 400 further comprises a first heater (426)extending between points X and Y, which may be referred to herein asheater XY. Optionally, MZI 400 may comprise a second heater (436)extending between points X′ and Y′, which may be referred to herein asheater X′ Y′. Heaters XY and X′Y′ can have a selected configuration,such as those shown in the context of FIGS. 4-8 above.

First arm BR comprises a multitude of waveguide segments parameterizingthe optical path along the waveguide and denoted in sequence as BC, CD,DE, EF, GH, HI, LI, JK, KL, LM, NO, OP, PQ, and QR, such that eachsegment is optically connected to the next optical segment in thesequence. Similarly, second arm B′R′ comprises a multitude of waveguidesegments parameterizing the optical path along the waveguide and denotedin sequence as B′C′, C′D′, D′E′, E′F′, G′H′, H′I′, I′J′, J′K′, K′L′,L′M′, N′O′, O′P′, P′Q′, and Q′R′, such that each segment is opticallyconnected to the next optical segment in the sequence.

In one embodiment, MZI 400 is rotationally symmetric such that the MZIis invariant under a 180 degree rotation about point W. In particular,in this embodiment, when rotated by 180 degrees about point W, the firstarm (401) BR would coincide with second arm (402) B′R′. Furthermore, inthis rotationally symmetric embodiment, each of the segments BC, CD, DE,EF, FG, GH, HI, LI, JK, KL, LM, MN, NO, OP, PQ, and QR would coincidewith segments B′C′, C′D′, D′E′, E′F′, F′G′, G′H′, H′I′, I′J′, J′K′,K′L′, L′M′, M′N′, N′O′, O′P′, P′Q′, and Q′R′, respectively.

When heated, first heater (426) XY causes an increase in the temperatureof waveguide segment HI and waveguide segment OP that is substantiallygreater than the increase in temperature of waveguide segment D′E′ andwaveguide segment K′L′. In other words, when heated, the first heatercauses the average temperature of segments HI and OP to be greater thanthe average temperature of segments D′E′ and K′L′. The difference inaverage temperatures is herein referred to as the relative temperaturedifference caused by the XY heater. The waveguide segments HI and OP areherein referred to as the heated waveguide segments because they aresubstantially heated by heater XY. Likewise, waveguide segments D′E′ andK′L′ are herein referred to as unheated segments because they are onlyweakly heated by heater XY.

As a consequence of the relative temperature difference between variouswaveguide segments caused by heater XY, light propagation through firstarm (401) BR from B to R will be shifted in phase relative to lightpropagation through second arm (402) B′R′ from B′ to R′. The amount ofrelative phase difference is proportional to the relative temperaturedifference referenced to above. The amount of relative phase differenceis also proportional to the sum of the lengths of the two heatedwaveguide segments HI and OP.

The power used to generate a predetermined relative temperaturedifference is proportional to the length of heater XY and the value ofthe predetermined relative temperature difference. Thus, as a firstorder approximation, the relative phase difference referred to above isindependent of the length of heater XY when expressed as beingproportional to the power applied to heater XY and also depends on thevarious details of the heater and nearby waveguide segments. Therelative phase difference divided by the heater power is referred toherein as the heater efficiency.

A significant consideration for obtaining desirable performance of theMZI is the configuration of first arm BR and second arm R′B′ to have nopoints of intersection and sections that are sufficiently close to causeexcessive optical coupling between the respective sections. For thesymmetric embodiment in FIG. 15, the geometrical details to ensure thedesired conditions are met are described below. Waveguide segments CF,Q′N′, G′J′, and JM are designated to be arcs of circles with commoncenter of curvature Z. In other words, waveguide segments CF, N′Q′, G′J′and JM are designated to be arcs of concentric circles. Because MZI 400is invariant under a 180 degree rotation about point W, waveguidesegments C′F′, NQ, G′J′, and J′M′ are consequently arcs of circles witha common center of curvature Z′, where Z′ corresponds to the point Zafter being rotated by 180 degrees about the point W. Furthermore, theradius of curvature of the segment CF is larger than the radius ofcurvature of segment N′Q′; the radius of curvature of segment N′Q′ islarger than the radius of curvature of segment G′J′; and the radius ofcurvature of segment G′J′ is larger than the radius of curvature ofsegment JM.

A suitable configuration is to form CF segment and the N′Q′ segment witharcs that have an angular extent between about 175 degrees and about 185degrees. A suitable configuration is to form JM segment and G′J′ segmentwith arcs that have an angular extent between about 225 degrees andabout 270 degrees. These arcs (CF, N′Q′, G′J′, JM-C′F′, NQ, GJ, J′M′)should be connected to their respective rotated arcs buy segments MN,M′N′, FG and F′G′ that may be straight or may have slight variationsfrom straight waveguides to allow connections to the arcs with littleloss by avoiding bends and so forth. These arcs are connected to thevarious ports of the input coupler and output coupler by segments BC,B′C′, QR and Q′R′ that may be straight or may have slight variationsfrom straight waveguides to allow connections to the arcs with littleloss by avoiding bends and so forth. Many small variations from theseprescribing design parameters may be introduced without affecting theintent of the design and will be so recognized by a person of ordinaryskill in the art. For example, small straight sections may be insertedwithin a segment that is comprised primarily of an arc of a circle. Asanother example, a segment that is described as being an arc of a circleherein may be replicated with a curve that has a somewhat varying radiusof curvature without affecting the intent of the design.

Additional features consistent with obtaining designable performance ofthe symmetric MZI of FIG. 15 impose restrictions on the various radii ofcurvature of the arcs discussed above. First, for improved heaterefficiency, the separation between HI segment and OP segment should beas small as consistent within the constraint imposed by the largestacceptable optical crosstalk between adjacent optical waveguides.Constrained by the selected separation limits to obtained no moreoptical crosstalk than a selected cutoff value, greater heaterefficiency generally is achieved by maintaining a constant separationbetween the HI segment and the OP segment. Thus, the separation betweenpoints H and I and between points O and P would be approximately equal.Furthermore, heater (426) XY should be centered approximately midwaybetween the HI and OP segments, e.g., see FIGS. 4-8.

In addition, the separation between the D′E′ segment and heater XYshould be substantially larger than the separation between the OP heatedwaveguide segment and the XY heater. Likewise, the separation betweenthe K′L′ unheated waveguide segment should be substantially larger thanthe separation between the HI heated segment and the XY heater. Theserelationships follow because the relative phase difference referred toabove is proportional to the temperature difference between the unheatedsegments and the heated segments. A suitable configuration to make theD′P (and E′O) distance approximately equal to the HL′ (and IK′)distance, both of which can be at least about 50 microns larger than thePH (and OI) distance. These conditions on the various separations can bemet by selecting appropriate values for the radii of curvature for eachof the curved sections mentioned above. Values of the various radii ofcurvature that were determined experimentally for devices comprisingsilica waveguides with 1.8% index contrast are as follows—suitable radiiof curvature for segments D′E′, OP, HI and K′L′ are 1.500 mm, 1.410 mm,1.390 mm, and 1.300 mm, respectively. Values within 20% of these values(±20%) would also be very effective of devices comprising silicawaveguides with a 1.8% index contrast. Values that are less than 80% ofthese values may still be effective, but may show some noticeablepenalty caused by excessive optical loss caused by optical propagationaround tight bends. Values that are more than 120% of these values maystill be effective, but may show some have a size that is larger than anequivalent design with the same performance. One skilled in the artwould be able to modify these values for any appropriate index contrast.Also, a person of ordinary skill in the art would recognize thatadditional values and ranges of values within the explicit ranges above,such as the 10% variation range) are contemplated and are within thepresent disclosure.

Particular features of an MZI as described above can be furtherdescribed with respect to the optical transfer function of either thebar path (that is the optical path between points A and S, or,equivalently, between points A′ and S′) or the cross path (that is theoptical path between points A and A′, or, equivalently, between points Sand S′). When no heat applied to either the XY heater or the X′Y′heater, an MZI that is symmetric in design with respect to theinput/output couplers and with respect to the two MZI arms, the opticaltransfer function of the bar path is close to zero and the opticaltransfer function of the cross path is close to unity. In such a design,with no heat applied to either the XY heater or the X′Y′ heater, themajority of the light, regardless of wavelength, travels through thecross path. In such a design, incrementally increasing the heat appliedto either the XY heater or the X′Y′ heater, incrementally reduces theamount of light that travels through the cross path and increases theamount of light that travels through the bar path. Although this featuremay be desirable for many applications, such as a normally dark variableoptical attenuator (VOA), other configurations may be more suitable forother applications. In one example, there may be an application inwhich, with no heat applied to either the XY heater or the X′Y′ heater,the majority of the light travels through the bar path. In anotherexample, there may be an application in which some wavelength dependencein the optical transfer function is desired. For such applications, aslight asymmetry in the MZI design may be preferred.

In a representative alternative embodiment, the MZI can be slightlyasymmetric such that the optical path length along the first arm BR isdifferent than the optical path along the second arm R′B′ by an amountthat is not greater than the wavelength of light intended for theapplication of the MZI One way to achieve the required optical pathlength difference is to provide the FG waveguide segment with a lengththat is different from the F′G′ waveguide segment such that the opticalpath length difference between the two segments has the desired value.This length adjustment is sufficiently small so that the designparameters described above meet their specified objectives. The opticalpath length difference may also be achieved by adjusting many othercombinations of lengths of various waveguide segments. The path lengthdifference can be effectively used for certain devices, such as awavelength dependent optical filter.

In another representative alternative embodiment, the MZI is moreasymmetric such that the optical path length along the first arm BR isdifferent from the optical path length align the second arm R′B′ by anamount that is greater than the wavelength of light intended for theapplication. An MZI that is asymmetric to such an extent has an opticaltransfer function with greater wavelength dependence, which is adesirable features for some applications, such as wavelength filtering.On way to achieve the specified optical path length difference is toprovide the FG waveguide segment with a length different form the F′G′segment such that the optical path length difference between the twosegments is the selected value. The optical path length difference maybe achieved by adjusting many other combinations of lengths of variouswaveguide segments. This length adjustment is still sufficiently smallso that the design parameters described above meet their desiredobjectives. For relatively large adjustments to the various waveguidesegments, additional adjustments may be correspondingly made to thedesign parameters described above to provide that the objectives areachieved. For symmetric or asymmetric embodiments, thermal simulation isone method for determining the performance of the embodiments for aparticular application and for determining other parameters necessary toprovide the desired device performance.

Various configurations for the XY heater are suitable for each of theembodiments described above. The XY heater may lie entirely between theOP segment and the HI segment such that no portion of the heater isdirectly above any portion of the OP segment or the HI segment.Alternatively, the XY heater may partially overlap both the OP segmentand the HI segment such that a fractional portion of the heater isdirectly above some portion of the OP segment and the HI segment. In yetanother alternative, the XY heater may completely overlap both the OPsegment and the HI segment such that some portion of the heater isdirectly above the entire portion of the OP segment and the HI segment.In yet another alternative, the XY heater may be a two segment heaterwith a first XY heater segment positioned at least partially over the OPwaveguide segment and the second XY heater segment positioned at leastpartially over the HI segment. The XY heater may be configured so thatit generates heat when current flows continuously from point X to pointY. Alternatively, the XY heater may be configured so that it generatesheat when current flows continuously from point Y to point X. In yetanother alternative embodiment, the XY heater may be configured so thatit generates heat when current enters the heater at a point midwaybetween X and Y and flows, in part towards point X and, in part towardspoint Y. These various configurations can correspondingly apply to theother arm wherein the corresponding segments are labeled with a prime(′). Also, these configurations can be further understood with referenceto FIGS. 4-12 that reference heater configurations in the context of anisolated waveguide arm.

To clarify some of the features illustrated in FIGS. 14 and 15, a subsetof the features is illustrated in FIG. 16, and FIGS. 17 and 18 presentalternative visual perspectives to emphasis various aspects of theembodiment. FIG. 16 illustrates the embodiment of the MZI in FIG. 14with second MZI arm 402 excluded for clarity. Referring to FIG. 16,advantageous relationships for some of the geometrical aspects of theMZI structure can be emphasized, which are explain in some detail withrespect to FIG. 15. As illustrated in FIG. 16, loopback waveguidesection 423 comprises extension segment 450 (MN of FIG. 15), loopportion 451 (JM of FIG. 15) and reversal segment 452 (IJ of FIG. 15).Extension segment 450 is depicted as a straight portion of waveguidebetween two marked points (JM of FIG. 15), although this straightcondition can be relaxed as noted above, and reversal segment 452 isbetween points I and J where J notes a transition point with respect tothe sign of the curvature of the waveguide path. Loop portion ispositioned between points J and point M. The end of extension segment450 can mark a point at which the radius of curvature becomes greaterthan the average radius of curvature of inner heated arc 422, which isR_(GJ) for the specific embodiment depicted in FIG. 16. Loopbackwaveguide section 433 of second arm 402 has equivalent sections asdescribed for loopback waveguide section 423 of first arm 401. Loopportion 451 of loopback waveguide section 423 is aligned with the arc ofa circle of radius R_(JM) that is centered at point Z. In addition,inner heated arc 422 of first MZI arm 401 is aligned with the arc of acircle of radius R_(GJ) that is centered at point Z′, and outer heatedarc 424 of first MZI arm 401 is aligned with the arc of a circle ofradius R_(NQ) that is also centered at point Z′. The midpoint between Zand Z′ is illustrated as point W in FIG. 16. In this embodiment, thevalue of R_(JM) smaller than the value of R_(GJ) by at least dR andR_(NQ)>R_(GJ). The value of 2 dW+sA is the center to center distancemarked in FIG. 16 between waveguides in loop portion 451 and waveguideextension 453 (FG in FIG. 15) at their point of closest approach in theembodiment of FIG. 16.

Waveguide extension 453 (FG in FIG. 15) is a straight waveguide sectionbetween points F and G in FIG. 16, and this waveguide section providesfor connecting inner heated arc 422 and outer arc 454. Outer arc 454 andwaveguide extension 453 provide for the rolled configuration allowingfor nesting of the two MZI arms in FIG. 14. While waveguide extension453 is shown as straight in the figures, waveguide extension 453 canhave some curvature with a large average radius of curvature to providefor the overall structure. Outer arc 454 (CF of FIG. 15) is depicted ascircular, but this condition can be relaxed without a significant changein the overall structure. If outer arc 454 is not precisely circular,radius R_(CF) can be considered the average radius.

To obtain the structure of FIG. 14 from the redacted structure in FIG.16, second arm 402 (not illustrated in FIG. 16) can be formed by takinga copy of first arm 401 at the identical initial location and rotatingthat copy 180 degrees about the point W illustrated in FIG. 16. With theaforementioned restrictions on the two radii of curvature, the loopbackpath of the phase shifter of second arm 402, thus formed, fits withinthe footprint of the first phase shifter and is substantially aligned toa circle that is smaller than and concentric with the circle to whichthe first phase shifter is aligned. The rotated structure is shown inFIG. 17 with the second waveguide shown with dashed lines. Furthermore,outer arc section 454 of first arm 401 between point CF has a convenientshape of a circular arc of radius centered at Z such that the arc has aradius, R_(CF), that is larger than the value of R_(JM) by at least dR.By forming the second arm as a copy of the first arm and rotating thecopy by 180 degrees, this restriction of the outer arc section is thereplicated waveguide section fitting outside of the first phase shifterand is substantially aligned to a circle that is larger than andconcentric with the circle to which the first phase shifter is aligned.

More generally, as shown by the dashed line in FIG. 17, second MZI arm402, thus formed, is rolled up within the region of first MZI arm 401without causing any optical impairment such as waveguide crossings orwaveguides that approach more closely than generally preferred accordingto the design rules associated with the particular PLC system used forthe MZI. By forming the second arm as a rotated version of a copy of thefirst arm, the optical path length for the first arm equal to theoptical path length of the second arm, although alternative embodimentsare discussed above with differences in the path lengths that break thesymmetry. Generally, an MZI having an optical path length for the firstarm equal to the optical path length of the second arm is referred to asa symmetric MZI. As known in the art, a general advantage of a symmetricMZI is that the configuration reduces the wavelength dependence of theMZI optical performance. But asymmetries can be introduced to provide agreater wavelength dependence in the performance, which can beadvantageous for appropriate devices.

FIG. 17 illustrates the MZI embodiment of FIG. 14 with the second armillustrated with a dashed line and omitting reference numbers forclarity and illustrates additional advantageous values for some of thegeometrical aspects of the MZI embodiment. In the context of thisfigure, we assume that heat is to be applied to the thermo-optic phaseshifter (heater) 426 on first arm 401. Since the function of this heateris to increase the temperature of the sections of first arm 401 relativeto second arm 402, it is desirable that all sections of second arm 402be located substantially far from heater 426 to keep the temperaturerise in these sections of second arm 402 to acceptable levels. Stated inother words, heater 426 for the thermo-optic phase shifter on first arm401 is considered to provide a thermal zone 460 around the heater duringits operation, in which the thermal zone note the region where theheating within a threshold value takes place. Outer curved heatedwaveguide section (outer heated arc) 424 and inner curved heatedwaveguide section (inner heated arc) 422 are appropriately situatedwithin thermal zone 460, and all sections of second arm 402 areappropriately situated outside thermal zone 460. To achieve thisperformance, it can be appropriate to have the sections of second arm402 that bound first heater 426 to have a separation, sP, that issubstantial and to have the first heater situated approximatelyequidistant from the two waveguide sections of second arm 402 on therespective sides of first heater 426.

The details of the materials used and other detailed features of thewaveguide design determine suitable numerical value for the preferredvalue for sP. Those skilled in the art can determine appropriaterestrictions for sP from thermal simulation or from experimentalmeasurement. For example, for silica channel waveguides with 1.8% indexcontrast formed on silicon substrates, in some embodiments it issuitable to have the sP value at least 100 microns and in furtherembodiments sP can be within the range from 200 microns to 400 microns.A person of ordinary skill in the art will recognize that additionalranges of sP within the explicit ranges above are contemplated and arewithin the present disclosure. Increasing the value of sP beyond 400microns, may cause an undesired increase the size of the MZI and offeronly very slight improvement in thermal efficiency. One configurationthat will provide the selected value of sP, is a configuration whereinR_(GJ)−R_(JM)>sP/2 and wherein R_(CF)−R_(NQ)>sP/2. Alternatively,various straight sections or other sections may be adjusted in lengthwhile maintaining R_(GJ)−R_(JM)=sW/2 and wherein R_(CF)−R_(NQ)=sW/2.

FIG. 18 schematically illustrates the loopback waveguide section 423 offirst arm 401 and loopback waveguide section 433 of second arm 402 ofthe MZI of FIG. 17. For clarity, the interior of the loopback waveguideon the first arm is shaded and the centers of curvature for the longestarc segments are illustrated with particular emphasis. When the phaseshifter is activated on the arm comprising the loopback waveguidesection 423 of first arm 401, the relative phase difference between thearms is driven in one direction and when the phase shifter is activatedon the arm comprising the loopback waveguide section 433 of second arm402, the relative phase difference between the arms is driven in theopposite directions. The opposing directions of these forces and thegeneral shape of this configuration may be remembered more easily byreferring to this configuration as a Yin Yang MZI.

FIG. 19 illustrates the compact nature of the Yin Yang MZI byillustrating that it can fit within a rectangular footprint with alength L and a width W. Reasonable ranges for these size parameters areset by the smallest acceptable radius of curvature for the loopbacksections of the respective waveguides and the closest distance ofwaveguides with acceptable levels of optical crosstalk. For a devicebased on silica waveguides with a 1.8% index difference, values oflength can be from about 4.8 mm to about 7.2 mm, and the width can befrom about 2.1 mm to about 3.1 mm.

Further embodiments of an MZI may be derived from the aforementionedembodiment of FIG. 19 by making adjusting the length, curvature and/orconfiguration of some of the waveguide sections such that theadjustments are small enough to preserve the desirable nesting featuredescribed above, but yet provides an optical path length differencebetween the first arm and the second arm that is a significant incomparison with the wavelength of light that is intended to propagatethrough the device. Generally, an MZI having an optical path length forthe first arm unequal to the optical path length of the second arm isreferred to as an asymmetric MZI. For one example, an MZI with anoptical path length difference between the first arm and the second armthat is on the order of four times smaller than the nominal wavelengthof light may be suitable for a push-pull VOA as described in U.S. Pat.No. 6,658,174B1. As a second example, an MZI with an optical path lengthdifference between the first arm and the second arm that is larger thanthe nominal wavelength of light may be useful in cases where increasedwavelength dependence is desirable.

As illustrated in FIG. 20, trenches can be placed within the planarlightwave circuit to reduce heat dissipation in the targeted waveguidesto further improve efficiency. Trenches in the planar structure, e.g., asilica glass structure, can be used to insulate the heated areas toprovide for further improvements in thermal efficiency and/or devicelayout. While the heater configuration can itself result in many of thedesired energy efficiencies, the trench can further improve efficienciesas well as reduce undesirable heating of adjacent unheated waveguides sothat unheated waveguides can be placed closer to heated waveguideswithout an undesirable reduction in temperature difference. FIG. 20shows a sectional view of a phase shifter 500 similar to that in FIG. 4with a pair of heated waveguide sections 501, 502 surrounded by cladding503 on optional substrate 504 with a heater 505 located on cladding 503and an optional coating 506, except for the inclusion of trenches 507,508 in the embodiment of FIG. 20. The trenches can be added similarlyfor efficiency to the embodiments in FIGS. 4-8 or other suitable heaterdesigns. The trenches can have a width across the plane of the PLCperpendicular to the center of the trench for a silica waveguide with a1.8% index difference from about 30 microns to about 50 microns, infurther embodiments from about 15 microns to about 100 microns, and inother embodiments from about 5 microns to about 200 microns. The trenchgenerally extends through any cladding, through to a distance below thecore depth of the waveguides. The length of the trenches can extendparallel to the heater for the lengths of the thermal zone. A person ofordinary skill in the art will recognize that additional ranges oftrench dimensions within the explicit ranges below are contemplated andare within the present disclosure.

FIGS. 21-24 illustrate a variety of input coupler (splitter)configurations that may be used with the MZI described herein, althoughother configures can be used as desired. FIG. 21 illustrates a Y-branchcoupler 530 with an input waveguide 532, first output waveguide 534 andsecond output waveguide 536. FIG. 22 illustrates a directional coupler540 comprising a first waveguide 542 and a second waveguide 544 thatapproach closely at a coupling zone 546 to provide for desired couplingbetween an input waveguide segment 548 and output waveguide segments550, 552. FIG. 23 illustrates a 1×2 multimode interference (MMI) device560, and FIG. 24 illustrates a 2×2 MMI 662. MMI are designed with singlemode waveguides optically coupled with a multimode region designed toallow interference to provide the desired coupling (or splittingfunction). Referring to FIG. 23, output waveguides 564, 566 connect toinput waveguide 568 through multimode region 570. Referring to FIG. 24,output waveguides 572, 574 couple to input waveguides 576, 578 throughmultimode region 580. The use of MMI as couplers/splitter for MZIgenerally are discussed in published U.S. patent application2012/0062900 to Langley et al., entitled “Optical Waveguide Splitters,”incorporated herein by reference. Additional variations on couplers notillustrated include, for example, a stabilized coupler and an adiabaticcoupler. Any of these and other variations on couplers known in the artor developed in the future may be practiced within the MZI describedherein.

FIGS. 25-28 illustrate a variety of output coupler configurations thatmay be used with the MZI described herein, which are analogous to theinput splitter embodiments in FIGS. 21-24. FIG. 25 illustrates aY-branch coupler 590 with input waveguides 592, 594 coupled to outputwaveguide 596. FIG. 26 illustrates a directional coupler 600 comprisinga first waveguide 602 and a second waveguide 604 that approach closelyat a coupling zone 606 to provide for desired coupling between an outputwaveguide segment 608 and input waveguide segments 610, 612. FIG. 27illustrates a 1×2 MMI 620 comprising input waveguides 622, 624 connectto output waveguide 626 through multimode region 628. FIG. 28illustrates a 2×2 MMI 630 comprising input waveguides 632, 634 couple tooutput waveguides 636, 638 through multimode region 640. Additionalvariations on output coupler designs not illustrated include, forexample, a stabilized coupler and an adiabatic coupler. Any of theseoutput coupler designs and other variations known in the art ordeveloped in the future may be practiced within the MZI describedherein.

The materials for forming the PLC can be deposited on a substrate usingCVD, variations thereof such as PECVD, flame hydrolysis or otherappropriate deposition approach. Suitable substrates include, forexample, materials with appropriate tolerance of higher processingtemperatures, such as silicon, ceramics, such as silica or alumina, orthe like. In some embodiments, suitable silicon dioxide precursors canbe introduced, and a silica glass can be doped to provide a desiredindex of refraction and processing properties. Similar, deposition anddoping can be performed for other optical materials. The patterning canbe performed with photolithography or other suitable patterningtechnique. For example, the formation of a silica glass doped with Ge, Pand B based on plasma enhanced CVD (PECVD) for use as a top claddinglayer for a PLC is described in U.S. Pat. No. 7,160,746 to Zhong et al.,entitled “GEBPSG Top Clad for a Planar Lightwave Circuit,” incorporatedherein by reference. Similarly, the formation of a core for the opticalplanar waveguides is described, for example, in U.S. Pat. No. 6,615,615to Zhong et al., entitled “GEPSG Core for a Planar Lightwave Circuit,”incorporated herein by reference. The parameters for formation of anappropriate waveguide cores and cladding are known in the art.

The PLC can be configured with optical connectors at or near edges ofthe structure to provide for coupling to an optical fiber or otherexternal light channel or waveguide. Thus, the PLC can be integratedwith other optical structures of an optical telecommunications networkas desired. The PLC with the MZI can be packaged appropriately forhandling. The PLC can provide for reduced energy consumption for opticalnetwork facilities.

The more efficient device can be packaged with respective opticalcouplers/splitters at the ends of the Mach-Zehnder interferometer toform a stand-alone product, or this component can be integrated into amultidevice planar lightwave circuit (PLC).

The embodiments above are intended to be illustrative and not limiting.Additional embodiments are within the claims. In addition, although thepresent invention has been described with reference to particularembodiments, those skilled in the art will recognize that changes can bemade in form and detail without departing from the spirit and scope ofthe invention. Any incorporation by reference of documents above islimited such that no subject matter is incorporated that is contrary tothe explicit disclosure herein. To the extent that specific structures,compositions and/or processes are described herein with components,elements, ingredients or other partitions, it is to be understand thatthe disclosure herein covers the specific embodiments, embodimentscomprising the specific components, elements, ingredients, otherpartitions or combinations thereof as well as embodiments consistingessentially of such specific components, ingredients or other partitionsor combinations thereof that can include additional features that do notchange the fundamental nature of the subject matter, as suggested in thediscussion, unless otherwise specifically indicated.

What is claimed is:
 1. A planar lightwave circuit comprising aMach-Zehnder interferometer along a plane of the circuit, theMach-Zehnder interferometer comprising: an input optical coupler; anoutput optical coupler; a first optical waveguide arm opticallyconnecting between the input optical coupler and the output opticalcoupler, the first optical waveguide arm comprising an outer curvedheated section, an inner curved heated section, and a loopback waveguidesection connecting the outer curved heated section and the inner curvedheated section, wherein the outer curved heated section and inner curvedheated section are adjacent each other with the inner curved heatedsection having a smaller average radius of curvature than the outercurved heated section and a larger average radius of curvature than theloopback waveguide section such that an open accessible space is formedenclosed in part by the arc of the inner curved heated section; a firstheater configured to heat both the outer curved heated section and theinner curved heated section of the first optical waveguide arm; and asecond optical waveguide arm not heated significantly by the firstheater and optically connected between the input optical coupler and theoutput optical coupler, the second optical waveguide arm comprising anouter curved section, an inner curved section adjacent the outer curvedsection and a loopback waveguide section, at least a portion of theloopback waveguide of the second optical waveguide arm being located inthe open accessible space of the first optical waveguide arm.
 2. Theplanar lightwave circuit of claim 1 comprising silica glass.
 3. Theplanar lightwave circuit of claim 1 wherein the first heater has anassociated thermal zone and wherein all waveguide portions within thethermal zone are curved.
 4. The planar lightwave circuit of claim 1wherein the first heater is positioned in the plane between the outercurved heated section and the inner curved heated section adjacent theouter curved heated section of the first waveguide arm, the relativepositions of the adjacent sections specifying inner edges of theadjacent waveguide sections closest to the adjacent waveguide sectionand outer edges furthest from the adjacent waveguide sectionperpendicular to the light path, and with an extent of the heater in theplane no further than the outer edges of the adjacent sections of thefirst waveguide arm.
 5. The planar lightwave circuit of claim 1 whereinthe first heater is positioned in the plane between the outer curvedheated section and the inner curved heated section adjacent the outercurved heated section of the first waveguide arm, the relative positionsof the adjacent sections specifying inner edges of the adjacentwaveguide sections closest to the adjacent waveguide section and outeredges furthest from the adjacent waveguide section perpendicular to thelight path, and with an extent of the heater in the plane such that thewidth of the heater is less than center to center distance between theadjacent waveguides.
 6. The planar lightwave circuit of claim 1 whereinthe first heater comprises two heater elements with a gap between theheater elements positioned in the plane of planar lightwave circuitbetween the adjacent heated waveguides.
 7. The planar lightwave circuitof claim 1 further comprising a second heater configured to heat both atleast a portion of the outer curved section and at least a portion ofthe inner curved section of the second optical waveguide arm and whereinthe first optical waveguide arm is not heated significantly by thesecond heater.
 8. The planar lightwave circuit of claim 1 wherein theouter curved section and inner curved section of the second opticalwaveguide arm are adjacent each other with the inner curved sectionhaving a smaller average radius of curvature than the outer curvedsection and a larger average radius of curvature than the loopbackwaveguide section such that an open accessible space is formed by thesecond waveguide arm enclosed in part by the arc of the inner curvedsection, and at least a portion of the loopback waveguide of the firstoptical waveguide arm being located in the open accessible space of thesecond optical waveguide arm.
 9. The planar lightwave circuit of claim 1wherein the first optical waveguide arm and the second optical waveguidearm have unequal lengths.
 10. A planar lightwave circuit comprising aMach-Zehnder interferometer along a plane of the planar lightwavecircuit the Mach-Zehnder interferometer comprising: an input opticalcoupler; an output optical coupler; a first optical waveguide armoptically connecting between the input optical coupler and the outputoptical coupler comprising an outer curved heated section, an innercurved heated section adjacent the outer curved heated section, aloopback section connecting the outer curved heated section and theinner curved heated section, and an unheated outer arc section extendingfrom the inner curved heated section and orienting the connection withthe output optical coupler approximately parallel to and in an oppositedirection from the connection with the input optical coupler; a firstheater associated with the first waveguide arm, wherein the first heateris positioned to significantly heat both the outer curved heated sectionand the inner curved heated section of the first waveguide arm wherein aprojection of the heater in a plane of the waveguides is curved; and asecond optical waveguide arm optically connecting between the inputoptical coupler and the output optical coupler, wherein the secondoptical waveguide is not significantly heated by the heater.
 11. Theplanar lightwave circuit of claim 10 wherein all significantly heatedwaveguide sections are curved.
 12. The planar lightwave circuit of claim10 wherein a projection of the first heater into the plane of the firstwaveguide arm is positioned in the plane between two adjacent sectionsof the first waveguide arm, the relative positions of the adjacentsections specifying inner edges of the adjacent waveguide sectionsclosest to the adjacent waveguide section and outer edges furthest fromthe adjacent waveguide section perpendicular to the light path, and withan extent of the heater in the plane no further than the outer edges ofthe adjacent sections of the first waveguide arm.
 13. The planarlightwave circuit of claim 10 wherein the waveguides comprise coresformed from silica glass.
 14. The planar lightwave circuit of claim 10further comprising a second heater associated with the second waveguidearm.
 15. The planar lightwave circuit of claim 10 wherein the outercurved heated section and inner curved heated section are adjacent eachother with the inner curved heated section having a smaller averageradius of curvature than the outer curved heated section and a largeraverage radius of curvature than the loopback waveguide section suchthat an open accessible space is formed enclosed in part by the arc ofthe inner curved heated section.
 16. The planar lightwave circuit ofclaim 15 wherein the second optical waveguide arm comprises an outercurved section, an inner curved section adjacent the outer curvedsection and a loopback waveguide section, at least a portion of theloopback waveguide of the second optical waveguide arm being located inthe open accessible space of the first optical waveguide arm.
 17. Aplanar lightwave circuit comprising a Mach-Zehnder interferometer alonga plane of the circuit, the Mach-Zehnder interferometer comprising: aninput optical coupler; an output optical coupler; a first opticalwaveguide arm optically connecting between the input optical coupler andthe output optical coupler; a first heater on cladding over waveguidecores that is associated with the first waveguide arm, wherein aprojection of the first heater into the plane of the first opticalwaveguide arm is positioned in the plane between two adjacent sectionsof the first waveguide arm, the relative positions of the adjacentsections specifying inner edges of the adjacent waveguide sectionsclosest to the adjacent waveguide section and outer edges furthest fromthe adjacent waveguide section perpendicular to the light path, and withan extent of the heater in the plane no further than the outer edges ofthe adjacent sections of the first optical waveguide arm; and a secondoptical waveguide arm optically connecting between the optical splitterand the optical coupler, wherein the second optical waveguide is notsignificantly heated by the first heater.
 18. The planar lightwavecircuit of claim 17 wherein the first optical waveguide arm comprises acore formed form silica glass.
 19. The planar lightwave circuit of claim17 further comprising a second heater associated with the second opticalwaveguide arm wherein a projection of the second heater into the planeof the second optical waveguide arm is positioned in the plane betweentwo adjacent sections of the second waveguide arm, the relativepositions of the adjacent sections specifying inner edges of theadjacent waveguide sections closest to the adjacent waveguide sectionand outer edges furthest from the adjacent waveguide sectionperpendicular to the light path, and with an extent of the projection ofthe second heater in the plane no further than the outer edges of theadjacent sections of the second optical waveguide arm, and wherein thesecond heater does not significantly heat the first optical waveguidearm.
 20. The planar lightwave circuit of claim 19 wherein the projectionof the heaters in the plane of the optical waveguides is curved.